How Is Error Possible In Mathematics?

Often When Works At A Hard Question, Nothing Good Is Accomplished At The First Attack. Then One Takes A Rest, Long Or Short, And Sits Down Anew To The Work. During The First Half-hour, As Before, Nothing Is Found, And Then All Of A Sudden The Decisive Idea Presents Itself To The Mind.

It Is Often Said That Experiments Should Be Made Without Preconceived Ideas. That Is Impossible. Not Only Would It Make Every Experiment Fruitless, But Even If We Wished To Do So, It Could Not Be Done. Every Man Has His Own Conception Of The World, And This He Cannot So Easily Lay Aside. We Must, Example, Use Language, And Our Language Is Necessarily Steeped In Preconceived Ideas. Only They Are Unconscious Preconceived Ideas, Which Are A Thousand Times The Most Dangerous Of All.

One Does Not Ask Whether A Scientific Theory Is True, But Only Whether It Is Convenient.

If We Knew Exactly The Laws Of Nature And The Situation Of The Universe At The Initial Moment, We Could Predict Exactly The Situation Of The Same Universe At A Succeeding Moment.

What Is A Good Definition? For The Philosopher Or The Scientist, It Is A Definition Which Applies To All The Objects To Be Defined, And Applies Only To Them; It Is That Which Satisfies The Rules Of Logic. But In Education It Is Not That; It Is One That Can Be Understood By The Pupils.